lf a,b,c are the interior angles of a triangle , simplify the following :
(sin a)(sin b)+[sin(b+c)][sin(a+c)]
--------------------------------------------
(cos a)(sin b)-[cos(b+c)][sin(a+c)]
F.4 trigonometry problems
2011-04-09 5:24 pm
回答 (1)
2011-04-09 8:27 pm
✔ 最佳答案
sin (b + c) = sin (180 - a) = sin acos ( b + c) = cos (180 - a) = - cos a
sin (a + c) = sin (180 - b) = sin b
so the expression becomes (sin a sin b + sin a sin b)/[cos a sin b - (-cos a)(sin b)] = 2 sin a sin b/(cos a sin b + cos a sin b) = 2 sin a sin b/(2 cos a sin b) = tan a.
收錄日期: 2021-04-25 22:37:45
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20110409000051KK00170